Question

A scoop of ice cream has a 3 inch radius. How tall should the ice cream cone of the same radius be in order to contain all of the ice cream inside the cone?

Answer 1

12cm

Explanation:

The scoop of Ice Cream is in the shape of a circular solid which is a Sphere.

For the ice cream to fit into the cone, the volume of the cone must be equal to that of the sphere.

Radius of the Sphere=3cm

Volume of a Sphere =
`(4)/(3)\pi r^3`

Volume of a Cone=
`(1)/(3)\pi r^2h`

`(1)/(3)\pi X 3^2h=(4)/(3)\pi X 3^3\\(1)/(3)h=(4)/(3) X 3\\(1)/(3)h=4\\h=4 X 3=12cm`

The Cone of same radius must be 12cm tall.